Answer :
Answer: The domain is {-3, 0, 12, 27}
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Explanation:
First solve for x to get
y = (2/3)x - 1
y+1 = (2/3)x
(2/3)x = y+1
x = (3/2)*(y+1)
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Now plug the values given into y. Do so one at a time. Lets plug in y = -3
x = (3/2)*(y+1)
x = (3/2)*(-3+1)
x = 1.5*(-2)
x = -3
So the domain value x = -3 corresponds to the range value y = -3.
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Repeat for y = -1
x = (3/2)*(y+1)
x = (3/2)*(-1+1)
x = 1.5*0
x = 0
The domain value x = 0 corresponds to the range value y = -1
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Repeat for y = 7
x = (3/2)*(y+1)
x = (3/2)*(7+1)
x = 1.5*8
x = 12
The domain value x = 12 corresponds to the range value y = 7
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Repeat for y = 17
x = (3/2)*(y+1)
x = (3/2)*(17+1)
x = 1.5*18
x = 27
The domain value x = 27 corresponds to the range value y = 17
Just as the domain is the x values, the range is the y values. To null out any confusion, "y" is the same as "f(x)", if that is the notation you are using.
For each range value -3, -1, 7, and 17, we will have an x-value. To find the corresponding x to each y-value, we just plug in the range for y, one at a time, and solve for x.
Try it.